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Beta regression is a type of statistical analysis used for modeling dependent variables that are bounded on both sides, typically between 0 and 1. It is particularly useful for variables that represent proportions or percentages.
Link appropriateness (“deviance residuals vs. indices of observation”, at least for the logit link)
Models continuous random variables and assumes values are in (0, 1), such as rates, proportions, and concentration or inequality indices.
Dependent variable is beta-distributed.
Missing and outliers should be addressed to allow for model fitting.
Beta regression model function: g(μ_i )=x_i^T β=n_i where β=(β_1,...,β_k )⊤ is a k × 1 vector. (x_(i1 ),....,x_ik)⊤ is the vector of k regressors (or independent variables or covariates) and n_i is a linear predictor.
Link function g(μ)=log(μ∕(1-μ)).
Description:
This dataset was built with the purpose of helping students in shortlisting universities with their profiles. The predicted output gives them a fair idea about their chances for a particular university.
This dataset includes various information like GRE score, TOEFL score, university rating, SOP (Statement of Purpose), LOR (Letter of Recommendation), CGPA, research and chance of admit.
Variables - Attribute Information
The table contains a brief description of the dataset.
| Variable | Parameter | Range | D escription |
|---|---|---|---|
| GRE Scores | gre_score | 290 - 340 (340 scale) |
Quantifies a c andidate’s p erformance on the Graduate Record E x amination, with a maximum score of 340 |
| TOEFL Scores | to efl_score | 92 - 120 (120 scale) |
Measures English language p r oficiency, scored out of a total of 120 points |
| Un iversity Rating | universi ty_rating | 1 to 5 with 5 being the highest rating | Rates u n iversities on a scale from 1 to 5, indicating their overall quality and r eputation. |
| S tatement of Purpose (SOP) Strength | sop | 1 to 5 with 5 being the highest rating | Evaluates the strength and quality of a c andidate’s SOP on a scale of 1 to 5 |
| Letter of Reccomm endation (LOR) Strength | lor | 1 to 5 with 5 being the highest rating | Evaluates the strength and quality of a c andidate’s SOP and LOR on a scale of 1 to 5 |
| Under graduate GPA | cgpa | 6.8 - 9.92 (10.0 scale) |
Reflects a student’s academic p erformance in their un d ergraduate studies, scored on a 10-point scale |
| Research Ex perience | research | 0 or 1 | Indicates whether a candidate has research experience (1) or not (0). |
| Chance of Admit | chance _of_admit |
0.34 - 0.97 (0 to 1 scale) |
Represents the likelihood of a student being admitted, expressed as a decimal between 0 and 1 |
The application of beta regression models has provided valuable insights into predicting student admission probabilities.
The analysis highlights the significance of various factors, such as GRE scores, TOEFL scores, CGPA, university ratings, letters of recommendation, and research experience.
The models that combined these predictors with the lowest AIC values and the highest pseudo R-squared scores were deemed most effective.
This study not only contributes to the academic understanding of factors influencing university admissions but also offers practical implications for educational institutions and policy-making.